Synthesis of the optimal control of linear logical-dynamical systems under instant multiple switchings of the automaton part

We consider a dynamic system controlled by an automaton with memory. The continuous part of the system is described by linear differential equations and the logical (automaton) part is described by linear recurrence equations. The moments of the state change of the automaton part are not known in advance and they are determined in the process of optimization. Modes with instant multiple switchings of the automaton part are admitted. Based on sufficient optimality conditions, we develop a technique for the synthesis of a feedback control. The application of the technique is demonstrated in an example.